∵a,b为单位向量,∴|a|=|b|=1.∵向量(ta-(1-t)b)⊥向量a,∴ (ta-(1-t)b).a=0.ta^2-(1-t)b,a=0.ta^2-ab+tab=0.t*1-|a||b|cos120+t|a||b|cos120=0.t-(-1/2)-(t/2)=0.t/2+1/2=0.∴t=-1.|